Graph Houghton groups form a genuinely new family of Houghton-type groups with finiteness type F_{r-1} but not FP_r, and with explicit presentations of their pure subgroups.
Asymptotic mapping class groups of closed surfaces punctured along Cantor sets
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Asymptotically rigid mapping class groups of infinite graphs
Graph Houghton groups form a genuinely new family of Houghton-type groups with finiteness type F_{r-1} but not FP_r, and with explicit presentations of their pure subgroups.